A Near-Linear-Time Solver for Graph $p$-Laplacian Semi-Supervised Learning via Continuation in $p$
Graph-based semi-supervised learning (SSL) propagates a few labels over a similarity graph by minimizing a Dirichlet-type energy. The standard quadratic ($p=2$) energy reduces to a single graph-Laplacian solve, but it degenerates exactly where SSL is most useful when labels are scarce: gathering more unlabeled data drives the $p=2$ estimate to a near-constant function whenever $d\ge2$ (Nadler-Srebro-Zhou). Well-posedness requires the nonlinear $p$-Laplacian energy with $p>d$. Existing solvers reduce this to a sequence of weighted Laplacian solves, but their reference implementations use a direct sparse factorization or ichol-preconditioned CG instead. Plugging a near-linear Laplacian solv...
| Authors | Oren E. Livne |
|---|---|
| Primary category | cs.LG |
| Published | 3 July 2026 |
| Last updated at source | 3 July 2026 |
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